I What kind of information can we extract from this equation?

[Arman777]

In cosmology, we are using the Friedmann equations for the evolution of the universe. And we are using this equation a lot.

$$\frac{H^2}{H_0^2} = \Omega_ma^{-3} + \Omega_{\Lambda} + \Omega_ra^{-4}$$

If we write $a(t)$ in terms of z,

$$H(z) = H_0\sqrt{\Omega_m(1+z)^{3} + \Omega_{\Lambda} + \Omega_r (1+z)^{4}}$$

I wonder by evaluating this function, for different omega values, what kind of different information(s) we can obtain

 

[jedishrfu]

Perhaps you could try plotting it in MATLAB and see what you get.

 

[Arman777]

Perhaps you could try plotting it in MATLAB and see what you get.

Yes but how it can changes things. I mean basically I am asking that if H(z) changes differently (w.r.t density paramters) what changes in the universe.

 

[jedishrfu]

I don't think you can deduce much more than the properties of space on the large scale and how it changes.

https://en.wikipedia.org/wiki/Friedmann_equations

and here's some seminar slides on it and its implications:

https://uncw.edu/phy/documents/thefriedmannequations.pdf

There's some numerical modeling at the end of the seminar slides.